Download DuctSIM User`s Manual - Mine Ventilation Services, Inc.

DuctSIM User’s Manual
Mine Ventilation Services
1625 Shaw Ave., Suite 103
Clovis, CA 93611 USA
Phone: 1-(559) 452-0182
Fax: 1-(559) 452-0184
Email: [email protected]
Table of Contents
1
INTRODUCTION ....................................................................................................................................... 1
1.1
1.2
1.3
DESCRIPTION ........................................................................................................................................ 1
FILES TYPES ......................................................................................................................................... 1
OPERATING SYSTEM AND REQUIREMENTS ........................................................................................... 1
2
LIST OF PROGRAM VIEWS ................................................................................................................... 2
3
DATA INPUT .............................................................................................................................................. 3
3.1
3.2
UNITS ................................................................................................................................................... 3
DUCT DETAILS DIALOG BOX................................................................................................................ 3
3.2.1
Resistance Data .................................................................................................. 4
3.2.1.1 Atkinson Friction Factor and Resistance Theory........................................... 5
3.2.1.1.1 Spiral Wound Steel Duct ......................................................................... 8
3.2.1.1.2 Fibreglass Duct ........................................................................................ 8
3.2.1.1.3 Flexible Force Duct/Bag .......................................................................... 9
3.2.1.1.4 Flexible Exhaust Duct .............................................................................. 9
3.2.2
Leakage Data and Network Theory ................................................................. 10
3.2.2.1 Hardy Cross Iterative Technique ................................................................. 10
3.2.2.2 Series-Parallel Method ................................................................................. 11
3.2.2.3 Resistance of Leakage Paths ........................................................................ 12
3.2.3
Zones ................................................................................................................ 14
3.2.4
General ............................................................................................................. 15
3.2.4.1 Forcing Versus Exhausting Duct Systems ................................................... 15
3.2.5
Input Data Ranges ............................................................................................ 18
3.3
3.3.1
3.4
SHOCK LOSS DETAILS ........................................................................................................................ 18
Shock Loss Theory .......................................................................................... 20
FANS .................................................................................................................................................. 24
3.4.1
General Details................................................................................................. 24
3.4.1.1 Auxiliary Fan Installation Guidelines .......................................................... 24
3.4.2
Inputting Fans in the DuctSIM Program .......................................................... 24
3.4.3
Fan Curves ....................................................................................................... 26
3.4.3.1 Fan Stall ....................................................................................................... 29
3.4.3.2 Pressure Gradients ....................................................................................... 30
3.4.4
Fan Laws .......................................................................................................... 32
3.4.5
Fan Database .................................................................................................... 32
3.4.6
Fixed Pressure Fans ......................................................................................... 34
3.5
3.6
3.7
4
VIEWING THE RESULTS ..................................................................................................................... 37
4.1
4.2
4.3
4.4
4.5
5
INPUT VIEW........................................................................................................................................ 34
FIXED QUANTITY TOOL...................................................................................................................... 35
NOTEPAD............................................................................................................................................ 36
RESULTS VIEW ................................................................................................................................... 37
FAN RESULTS VIEW ........................................................................................................................... 37
FAN CURVE VIEW .............................................................................................................................. 38
GRAPH VIEW ...................................................................................................................................... 39
PRINTING ............................................................................................................................................ 41
REFERENCES .......................................................................................................................................... 43
APPENDIX A – MEASURED DATA ............................................................................................................... 45
APPENDIX B – DUCTCON PROGRAM ........................................................................................................ 48
i
List of Figures
FIGURE 1: TOOL BUTTONS FOR VIEWS ........................................................................................................................ 2
FIGURE 2: UNIT CONVERSION TOOL ........................................................................................................................... 3
FIGURE 3: DUCT DETAILS DIALOG BOX ...................................................................................................................... 4
FIGURE 4: PRESET DIAMETER LIST DIALOG BOX ........................................................................................................ 5
FIGURE 5: PRESET ATKINSON FACTOR DIALOG BOX................................................................................................... 5
FIGURE 6: FIGURE SHOWING TYPICAL TYPES OF DUCT (FROM SCHAUENBURG FLEXADUX CORPORATION) ............... 8
FIGURE 7: SKETCH OF THE MESHES IN A SIMPLE DUCT SYSTEM ............................................................................... 11
FIGURE 8: NETWORK DIAGRAM FOR SERIES-PARALLEL SOLUTION OF VENTILATION NETWORKS ............................ 12
FIGURE 9: EXPLANATION OF THE ZONES CONCEPT ................................................................................................... 14
FIGURE 10: TYPICAL FORCE VENTILATION SYSTEM.................................................................................................. 16
FIGURE 11: TYPICAL EXHAUST VENTILATION SYSTEM ............................................................................................. 16
FIGURE 12: REDUCTION IN AIR VELOCITY WITH DISTANCE - EXHAUST DUCT (AFTER BLACK ET AL., 1978) ............ 17
FIGURE 13: TYPICAL EXHAUST DUCT WITH FORCE OVERLAP ................................................................................... 17
FIGURE 14: TYPICAL FORCING DUCT WITH EXHAUST SCAVENGER ........................................................................... 18
FIGURE 15: SHOCK LOSS DATA DIALOG BOX ........................................................................................................... 19
FIGURE 16: FAN INPUT VIEW..................................................................................................................................... 24
FIGURE 17: ADD FAN DIALOG BOX ........................................................................................................................... 26
FIGURE 18: FAN CURVE DIALOG BOX ....................................................................................................................... 27
FIGURE 19: EXAMPLE FAN CURVE ............................................................................................................................ 28
FIGURE 20: FAN CURVE SHOWING SELECTION OF POINTS AND INTERPOLATION....................................................... 29
FIGURE 21: TYPICAL PRESSURE PROFILES ALONG A DUCT ....................................................................................... 31
FIGURE 22: FAN DATABASE VIEW............................................................................................................................. 33
FIGURE 23: SELECT FAN TO ADD TO PROJECT DIALOG BOX ..................................................................................... 34
FIGURE 24: INPUT VIEW ............................................................................................................................................ 35
FIGURE 25: FIXED QUANTITY TOOL DIALOG BOX..................................................................................................... 36
FIGURE 26: NOTEPAD ................................................................................................................................................ 36
FIGURE 27: RESULTS VIEW ....................................................................................................................................... 38
FIGURE 28: FAN RESULTS VIEW ................................................................................................................................ 38
FIGURE 29: FAN CURVE VIEW ................................................................................................................................... 39
FIGURE 30: GRAPH PREFERENCES DIALOG BOX........................................................................................................ 40
FIGURE 31: GRAPH VIEW .......................................................................................................................................... 41
FIGURE 32: PRINT PREVIEW FROM THE FAN INPUT VIEW .......................................................................................... 42
FIGURE 33: PRINT PREVIEW FROM THE FAN RESULTS VIEW ..................................................................................... 42
FIGURE 33: DUCTCON ADD DUCT DATA DIALOG BOX ............................................................................................. 48
FIGURE 34: DUCTCON INPUT VIEW ........................................................................................................................... 49
FIGURE 35: DUCTCON RESULTS VIEW ....................................................................................................................... 50
List of Tables
TABLE 1: ATKINSON FRICTION FACTOR VALUES FOR TYPICAL DUCTS ....................................................................... 7
TABLE 2: TYPICAL LEAKAGE RESISTANCE PER 100 M OR 100 FT OF DUCT................................................................ 13
TABLE 3: SHOCK LOSS COEFFICIENTS INCORPORATED IN THE DUCTSIM PROGRAM (AFTER ASHRAE, 1989) ........ 23
TABLE 4: AUXILIARY FAN INSTALLATION GUIDELINES (AFTER JM AEROFOIL FANS, 1999) ..................................... 25
TABLE 5: FAN LAWS ................................................................................................................................................. 32
TABLE 6: LOG-LINEAR TRAVERSE POSITIONS IN A CIRCULAR DUCT (AFTER MCPHERSON 1993) ............................. 46
TABLE 7: PSYCHROMETRIC RELATIONSHIPS .............................................................................................................. 47
TABLE 8: LIST OF SYMBOLS FOR THE PSYCHROMETRIC CALCULATIONS ................................................................... 47
ii
List of Equations
4A
........................................................................................ 5
Per
EQUATION 1 – HYDRAULIC MEAN DIAMETER:
d=
EQUATION 2 – DARCY-WEISBACH EQUATION:
p = fL
EQUATION 3 – ATKINSON EQUATION:
Per u 2
......................................................................... 5
ρ
A 2
Per 2
u ........................................................................................... 6
A
fρ
k = ........................................................................................... 6
2
p = kL
EQUATION 4 – ATKINSON FRICTION FACTOR:
p
................................................................................................................. 6
Q2
P
EQUATION 6 – AIRWAY RESISTANCE: R = kL er3 ............................................................................................... 6
A
ρ
EQUATION 7 – ATKINSON FRICTION FACTOR ADJUSTMENT: k a = k s a .............................................................. 6
ρs
1
2k
EQUATION 8 – VON KÁRMÁN EQUATION:
............................................... 7
=
f =
2
ρ


d
4 2 log 10   + 1.14
e


EQUATION 5 – SQUARE LAW:
R=
EQUATION 9 – HARDY CROSS TECHNIQUE:
EQUATION 10 – EQUIV. RESISTANCE (I):
EQUATION 11 – EQUIV. RESISTANCE (II):
EQUATION 12 – EQUIV. RESISTANCE (III):
Σ(2R i Q i + STi )
1
=
R n -(n +1)
R n -(n +1) =
(
1
R (n-1)-(n +1)
EQUATION 13 – SERIES-PARALLEL FAN PRESSURE:
EQUATION 14 – WORONIN’S EQUATION:
- Σ (R i Q i Q i − PTi )
∆Q m =
Rl =
....................................................... 11
1
1
............................................................. 12
+
Rp
RD
RD × Rp
Rp + RD
=
)
2
............................................................. 12
1
1
...................................... 12
+
Rp
R D + R n -(n +1)
2
........................................................... 12
Pfan = R ED × Q fan
 L 
Rd ×

 100 
3
  Q1  
3× 
- 1 


Q
2

 
2
.................................................................. 13
2

(P1 - P2 ) 
5
EQUATION 15 – BROWNING’S FORMULA: R d =

 .................................................... 13
L
 2Q 1 + 3Q 2 
ρ u2
EQUATION 16 – VELOCITY PRESSURE:
............................................................................................. 20
pv =
2
EQUATION 17 – SHOCK LOSS PRESSURE:
p shock = C p v ..................................................................................... 20
p
Cρ
EQUATION 18 – SHOCK LOSS RESISTANCE: R shock = shock
................................................................ 20
=
2
Q
2 A2
iii
Total Pressure = Static Pressure + Velocity Pressure ................... 30
ρ
EQUATION 20 – FAN PRESSURE ADJUSTMENT: Pa = Ps a ................................................................................. 32
ρs
EQUATION 19 – TOTAL PRESSURE:
EQUATION 21 – DUCT AIR VELOCITY:
EQUATION 22 – LEAKAGE COEFFICIENT:
1
Q=A
n
n
∑ u i ..................................................................................... 45
i =1
3(Q1 - Q 2 ) (P1 - P2 )
............................................................... 49
Lc =
2L(P11.5 - P21.5 )
Table of Symbols
Symbol
A
d
C
e
f
k
ka
ks
L
p
pshock
P1
P2
Pa
Per
Ps
PTi
Q
∆Qm
Qi
Q1
Q2
R
Description
Cross Sectional Area
Diameter or Hydraulic Mean Diameter
Shock Loss Coefficient
Height of Duct Asperities
Chezy Darcy Coefficient of Friction
Atkinson Friction Factor
Atkinson Friction Factor at Standard Air Density
Atkinson friction Factor at Actual Air Density
Length
Pressure Loss
Pressure Loss due to Shock Loss
Upstream Duct Total Pressure
Downstream Duct Total Pressure
Fan Total Pressure at Actual Air Density
Airway Perimeter
Fan Total Pressure at Standard Air Density
Fan Total Pressure in Branch “i”
Airflow Quantity
Hardy Cross Mesh Correction Factor - Quantity
Quantity in Branch “i”
Upstream Quantity
Downstream Quantity
Airway Resistance – General
Rd
RD
RED
Ri
Rl
Rp
Rshock
STi
u
ρ
ρa
ρs
Duct Resistance per 100 m (100 ft) Duct
Resistance for Each Duct Segment
Equivalent Resistance of the Entire Duct
Resistance of Branch “i”
Leakage Path Resistance per 100 m Duct
Resistance of Discrete Leakage Paths
Resistance due to Shock Loss
Slope of Fan Curve in Branch “i”
Air Velocity
Air Density
Actual Air density
Standard Air Density = 1.2
Unit
m2 (ft2)
m (ft)
Dimensionless
m (ft)
Dimensionless
kg/m3 (lbf min2/ft4)
kg/m3 (lbf min2/ft4)
kg/m3 (lbf min2/ft4)
m (ft)
Pa (in.w.g.)
Pa (in.w.g.)
Pa (in.w.g.)
Pa (in.w.g.)
Pa (in.w.g.)
m (ft)
Pa (in.w.g.)
Pa (in.w.g.)
m3/s (kcfm)
m3/s (cfm)
m3/s (kcfm)
m3/s (kcfm)
m3/s (kcfm)
Ns2/m8 [gaul]
(Practical Unit - P.U.)
Ns2/m8 (P.U.)
Ns2/m8 (P.U.)
Ns2/m8 (P.U.)
Ns2/m8 (P.U.)
Ns2/m8 (P.U.)
Ns2/m8 (P.U.)
Ns2/m8 (P.U.)
Pa/m3/s (in.w.g. / kcfm)
m/s (ft/min)
kg/m3 (lb/ft3)
kg/m3 (lb/ft3)
kg/m3 (lb/ft3)
iv
1
1.1
INTRODUCTION
Description
In any type of subsurface excavation, auxiliary ventilation systems represent a critical
component of the overall ventilation scheme. Without adequate secondary ventilation it is
impossible to provide sufficient air to dead-end headings, no matter what the quantity or
quality of air at the duct inlet. In modern mining and tunneling, face ventilation problems are
compounded by the large amounts of mechanized diesel equipment, and longer overall
development. The increased use of diesel engines results in heat, gas and diesel particulate
matter, and the generally deeper excavations leads to higher strata heat loads.
With the advent of personal computers, and user-friendly operating systems, the use of
ventilation simulation programs has become increasingly popular for designing, optimising,
upgrading and maintaining primary (main) ventilation systems. The DuctSIM program has
been designed to assist with the simulation of auxiliary fan and duct systems. According to
input data, the user is able to construct models and optimise them by considering duct type
and diameter, shock losses, and the number, type and spacing of auxiliary fans. The program
may be used for initial design, or equally to help troubleshoot and improve existing duct
installations. This software has been designed for large subsurface duct installations
(predominantly for the mining and tunnelling industries), rather than industrial duct systems
in buildings. This document is more than a User’s Manual, it also provides background,
theory and empirical data relating to the design of auxiliary fan and duct systems.
1.2
Files types
DuctSIM supports two different file types. These are:
1. Duct files - *.dct
2. Fan database files - *.fdb
Duct files, designated by the extension *.dct, save all data that the user has input, including
any fans that have been designated for the particular duct. Fan database files represent data
archives for the development, manipulation and storage of fan curves.
1.3
Operating System and Requirements
DuctSIM has been developed for Windows XP, 2000, NT, and 95/98. The DuctSIM program
was developed using the Microsoft Visual C++ programming language in conjunction with
Stingray Software Company’s Objective Grid program. The compiled applications contain all
necessary libraries to function successfully within the aforementioned Windows operating
environments. The screen resolution should be set to at least 800 × 600 pixels for optimum
viewing.
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2
LIST OF PROGRAM VIEWS
The DuctSIM program consists of seven main views. These views are accessed from either
the View Menu or by pressing the large tool buttons shown in Figure 1. These views are
briefly discussed below, and are detailed throughout the manual:
Figure 1: Tool Buttons for Views
•
•
•
•
•
•
•
The Input View summarizes the data entered by the user. Data is entered via the Duct
Details and Shock Loss dialog boxes, and the Fan Input View.
The Fan Input View allows the user to enter details for all the fans specified in the
duct.
The Results View summarizes the main results for the simulation.
The Fan Results View provides a detailed list of all the fans and their predicted
operating characteristics.
The Fan Curve View. This split view shows the operating characteristics for each
selected fan. The data is presented in a table and also graphically.
The Graph View provides a visual trend for airflow and pressure distributions
throughout the length of the duct. The user may select either quantity or velocity for
the airflow trend, and total pressure and/or static pressure for the pressure trend. The
user may also show a schematic of the duct configuration. This includes the airflow
direction, location and number of fans, the location of the various shock losses and the
entry and exit configurations.
The Fan Database View. This is a separate section of the DuctSIM program that is
shown only when the user either opens an existing fan database file, or generates a
new one.
Data entry is via a series of dialog boxes. Dialog boxes are input forms that force the user to
enter sensible data to fully describe the duct.
All of these views will be detailed in the following sections in the context of data input
(Section 3) and the viewing of results (Section 4).
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2
3
DATA INPUT
3.1
Units
The DuctSIM program allows users to work in either Imperial or SI units. The user may
choose which units to work in when starting a new file, or may convert units in existing
databases by selecting the Unit Conversion tool from the Tools menu. In either case the
dialogue shown in Figure 2 is presented to the user.
Figure 2: Unit Conversion Tool
3.2
Duct Details Dialog Box
The DuctSIM program requires certain data to be input by the user. The physical
characteristics of the duct are entered in the Duct Details dialog box (Figure 3), and must be
entered whenever a new DuctSIM model is developed.
This dialog box consists of four tabbed pages, which are:
•
•
•
•
Resistance
Leakage
Zones
General
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3
Figure 3: Duct Details Dialog Box
3.2.1
Resistance Data
The Resistance page allows the user to enter the duct diameter, length, and Atkinson friction
factor. The duct diameter and friction factor may be entered directly, or selected from userdefined lists. Pressing the Edit buttons adjacent to the friction factor and diameter list boxes
provides access to the user-defined lists (see following figures). These dialog boxes allow the
user to allocate new values, and in the case of the Atkinson friction factor descriptions for
commonly used criteria.
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4
Figure 4: Preset Diameter List Dialog Box
Figure 5: Preset Atkinson Factor Dialog Box
If the duct is not round then the equivalent round diameter should be used. In the case of a
square or rectangular duct the hydraulic mean diameter should be applied to the duct. This is
evaluated from the following relationship (refer to the Symbols Table [page iv] for all
equations):
Equation 1 – Hydraulic Mean Diameter:
d=
4A
Per
3.2.1.1 Atkinson Friction Factor and Resistance Theory
The determination of frictional pressure drop in airways may be obtained from the following
relationship:
Equation 2 – Darcy-Weisbach Equation:
p = fL
Per u 2
ρ
A 2
This is a form of the Chezy-Darcy (also known as Darcy-Weisbach) Equation, and is
applicable to circular and non-circular airways and ducts. The Chezy-Darcy coefficient of
friction (dimensionless) varies with respect to Reynolds Number, the trend of which is plotted
DuctSIM Design Manual – Version 1.0b – October 2003
5
on the Moody diagram. The Darcy-Weisbach Equation was adapted by Atkinson to give the
following, commonly used Atkinson Equation:
Equation 3 – Atkinson Equation:
p = kL
Per 2
u
A
The Atkinson friction factor is a function of air density, and is computed as:
Equation 4 – Atkinson Friction Factor:
k=
fρ
2
Since the Chezy-Darcy coefficient of friction is dimensionless, the Atkinson friction factor
has the units of density (kg/m3). The Atkinson Equation may be expressed in terms of the
Atkinson resistance for the airway, where:
Equation 5 – Square Law:
R=
Equation 6 – Airway Resistance:
p
Q2
R = kL
Per
A3
The Square Law is an important relationship that is used to establish resistance from
measured pressure and quantity data. Equation 6 is used to determine resistance from typical
Atkinson friction factors, and known or proposed airway geometry. The units of resistance
are Ns2/m8, which is the same unit as the “gaul.” Imperial units of resistance are given in the
Practical Unit (P.U.), which is equivalent to 1 milli-inch Water Gauge / (1 kcfm)2. It should
be noted that the frictional pressure drop term in the Square Law is directly proportional to air
density, as is the Atkinson friction factor. Hence, the Atkinson friction factor that is applied
must be adjusted for actual mine air density. The adjustment is arrived at using the following
relationship:
Equation 7 – Atkinson Friction factor Adjustment: k a = k s
ρa
ρs
When using the Atkinson friction factor it is important to remember that the factor is not
constant for a given airway, but varies with Reynold’s Number. However, in mine ventilation
it normal to assume that the Atkinson friction factor is constant, regardless of the flow
regime. This is because for fully turbulent flow (which is typically the case in mine and
tunnel ventilation) the friction factor is a function only of the relative roughness of the
airway. The relative roughness of the airway is defined as the height of the airway asperities
(e) divided by the hydraulic mean diameter. The Von Kármán Equation (McPherson, 1993)
gives the relationship for Atkinson friction factor, coefficient of friction and relative
roughness for fully turbulent flow, as follows:
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6
Equation 8 – Von Kármán Equation: f =
2k
ρ
=
1


d
4 2 log 10   + 1.14
e


2
From this equation it is apparent that for ducts with the same surface roughness (asperity
height), but different diameters, the Atkinson friction factor will vary. Hence, as the duct
diameter increases, and all other conditions remain the same, both the relative roughness and
the Atkinson friction factor will decrease.
Table 1 provides a list of typical friction factors for ventilation ducting. These are actual
measured friction factors for straight sections of ventilation duct in mines and tunnels. If the
user has reason to believe that the duct will not be straight, then it is advised that an
installation or roughness correction factor be applied. Typical references (Wolski and Barry,
1997) suggest that this correction factor should be in the range of 1.3 to 1.4 (30 to 40%
higher).
Figure 6 shows photographs of the duct types provided in Table 1, which are the most
commonly used for underground construction activities.
Duct Type
Steel Duct
Galvanized spiral wound
Mild steel, smooth bore duct
Fibreglass duct
Force Duct/Bag
Light Duct
Heavy duct – Small
TBM Cassette Duct
Face Ventilation – Very Poor Installation
Reinforced Flexible Duct
Flexible Exhaust Duct – Excellent Installation
Flexible Exhaust Duct – Slack
kg/m3 (x10-10 lbf min2/ft4)
k Factor
Coefficient of
Friction
0.004 (21.6)
0.003 (16.2)
0.003 (16.2)
0.007
0.005
0.005
0.003
0.004
0.004
0.025
(16.2)
(21.6)
(21.6)
(135)
0.005
0.007
0.007
0.042
0.004 (21.6)
0.010 (53.9)
0.007
0.017
Table 1: Atkinson Friction Factor Values for Typical Ducts
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7
Spiral Wound Steel Duct
Fibreglass Duct
Flexible Force Duct/Bag
Flexible Exhaust Duct
Figure 6: Figure Showing Typical Types of Duct (from Schauenburg Flexadux Corporation)
3.2.1.1.1 Spiral Wound Steel Duct
Spiral wound steel duct is used as both forcing and exhausting duct. Steel duct has the
advantage that it may be wound onsite, and many mines have a dedicated workshop for this
activity. The duct can be manufactured in different gauges to meet strength and cost
requirements. Typical diameters for this duct range from 150 to 2,450 mm (0.5 to 8 ft).
Overview:
• Lowest initial-cost suction duct
• Non-flammable
• Holds high positive and negative pressure
• Medium leakage
• Low friction factor
Best suited for:
• Moderate length ventilation runs (less than 3,000 m [10,000 ft])
• Single use applications (the duct will bend if dropped which will result in poor sealing
of the joints)
3.2.1.1.2 Fibreglass Duct
Fibreglass ducting is designed to withstand impact and high negative or positive pressures.
This rigid ducting is specified for critical applications with its main features being low
weight, excellent corrosion resistance, and high performance for easy installation and
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8
reusability. This duct is sometimes provided in an oval configuration where clearance is
limited. The typical size ranges from about 300 to 1,200 mm (1 to 4 ft). The typical duct
length is 6 meters (20 ft). The seals include neoprene for clean and acidic environments, no
seals for low-pressure applications and short runs and elastic seals for dusty environments.
Overview:
• Most durable suction duct
• Lightweight
• Holds high positive and negative pressure
• Low friction factor
• Medium Leakage
• Relatively expensive
Best suited for:
• Short-length ventilation run (less than 1,500 m [5,000 ft])
• Multiple reuse operations
• Mine development
3.2.1.1.3 Flexible Force Duct/Bag
Flexible force duct is also known as bag, or lay-flat ducting. This duct is designed for positive
pressure applications, and is the standard ducting used in hard-rock mines, due primarily to
low initial cost and ease of installation. Seams and grommets generally should be welded to
be airtight, and provide a low resistance to airflow. Typical diameters range from 150 to
2,450 mm (0.5 to 8 ft). The duct may also be provided in single lengths up to 300 meters
(1,000 ft) for applications such as tunnel boring machines (TBM). Many different grades of
material can be used to ensure that specific pressure and durability requirements are achieved.
Overview:
• High leakage in face ventilation. Relatively low leakage in TBM applications.
• Medium friction factor
• Many grades available
• Low cost
• Easy installation
Best suited for:
• All types of ventilation:
 Short ventilation runs for face ventilation
 Long ventilation runs, especially when using cassette-type systems for TBM
tunnels
3.2.1.1.4 Flexible Exhaust Duct
Flexible suction ducting is ideal for exhaust ventilation where a lightweight, easily
transportable duct is required. The duct is typically manufactured from PVC-coated nylon
and polyester, and reinforced with helical-wound spring steel. Standard diameters range from
150 to 1,500 mm (0.5 to 5 ft), with standard lengths of 3, 4.5, or 7.5 meters (10, 15, or 25 ft).
The pitch of the coiled steel spring can be varied as required.
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9
Overview:
• Weight dependent on negative pressure rating
• Can be stored in a small area
• If correctly tensioned medium friction factor, otherwise the frictional losses can be
very high
Best suited for:
• Starter tunnels
• Short ventilation runs
• Flexible connections in other type of ducting
3.2.2
Leakage Data and Network Theory
The leakage sheet (shown in Figure 3) features a slider allowing the user to select leakage
from a qualitative assessment of the duct installation (bad to excellent). The user may also
enter leakage resistance directly. This parameter is a resistance, given in Ns2/m8 per 100 m of
duct or Practical Units (P.U.) per 100 ft of duct (see Table 2).
It is inevitable that some degree of leakage will be associated with ventilation ducts. The
quantification and prediction of this leakage is complex, and has been the topic for significant
research during the last 50 years. Three basic methods exist for the analysis of flow problems
in leaky ducts:
1. Mathematical analysis for a duct with uniformly distributed leakage. This technique
uses a complex analysis that results in an integral that has to be solved numerically.
2. Assumption of a number of discrete leakage paths, enabling the treatment of the leaky
duct as a ventilation network. Typically this network problem would be solved using
an iterative technique such as the Hardy Cross.
3. Assumption of a number of discrete leakage paths, which enables the treatment of the
leaky duct as a series-parallel combination of airflows along the duct and through
leakage paths.
The DuctSIM program utilizes both the Hardy Cross technique and the Series-Parallel
method for solution of duct ventilation networks. The Hardy Cross method is used in all
instances except the case when the user elects to run the simulation with a fixed quantity. In
this scenario all fans are removed from the duct, and a simplified analysis is conducted using
the Series-Parallel method.
3.2.2.1 Hardy Cross Iterative Technique
The Hardy Cross technique involves making an initial estimate of the airflow distribution,
calculating an approximate correction to be applied to each branch, and then repeating the
correction procedure iteratively until an acceptable degree of accuracy is obtained. The
following equation is used to determine the correction that must be applied to each mesh in
the network:
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Equation 9 – Hardy Cross Technique:
∆Q m =
- Σ (R i Q i Q i − PTi )
Σ(2R i Q i + STi )
Unlike a traditional ventilation network simulation program, the DuctSIM program does not
feature a mesh selection routine. Because of the nature of a duct system, a simple network
can be developed that incorporates the duct, drift, duct leakage paths and the face. A twomesh network is shown in Figure 7. The DuctSIM program assumes that the drift and face
have a resistance of zero. This simplifies the analysis, and is justified by the fact that the
pressure losses associated with the duct are typically many orders of magnitude higher than
those found in the drift. This simplification only results in a significant error when the duct
penetrates a bulkhead or regulator. In this case there will be an appreciable resistance
associated with the structure in the drift that will not be accounted for.
MESH 1
Face
Leakage Path
D rift o r T u n n e l
MESH 2
Fan
D uct
Figure 7: Sketch of the Meshes in a Simple Duct System
For the network the number of meshes is equal to the number of discrete leakage paths plus
one. For the DuctSIM application the number of leakage paths is automatically set at 99, such
that the duct is broken down into 100 equal segments. This was found to represent a good
compromise between execution/computation time (increasing the number of high resistance
branches increases the number of iterations), and accuracy (too few leakage branches will not
adequately represent a long duct installation).
3.2.2.2 Series-Parallel Method
Figure 8 shows a network representation of a leaky duct. In this case the duct has “n” joints
or leakage paths, each of which has the resistance denoted by Rp. This effectively divides the
duct into “n+1” segments of equal length, each of which have been assigned a resistance of
RD. It is also assumed that:
•
•
The ambient pressure outside the duct is the same at all locations along the duct.
The face resistance is zero.
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Fan - Forcing
Duct
RD
4
n-1
n
n+1
QFACE
3
Leakage Path
Qfan
Pfan
RED
2
Rp
1
Drift or Tunnel
Figure 8: Network Diagram for Series-Parallel Solution of Ventilation Networks
From parallel resistance theory, the equivalent resistance of the final mesh at face is (denoted
by Rn-(n+1), which is the resistance from junction to “n” to “n+1”):
Equation 10 – Equiv. Resistance (i):
1
R n -(n +1)
1
1
+
RD
Rp
=
Which reduces to:
Equation 11 – Equiv. Resistance (ii):
R n -(n +1) =
(
RD × Rp
Rp + RD
)
2
If the next mesh is added, then the equivalent resistance of the last two meshes, from “n-1” to
“n+1”, becomes:
Equation 12 – Equiv. Resistance (iii):
1
R (n-1)-(n +1)
=
1
1
+
Rp
R D + R n -(n +1)
Hence, by repeating this process through all meshes the overall equivalent resistance of the
duct can be determined (termed RED). In the case of the DuctSIM program, the Series-Parallel
solution is only applied for a fixed quantity analysis, when the fan is assumed to be at the
start (0 m) of the duct (as shown in Figure 8). If the quantity at the fan is known, then the fan
requirement (total pressure) is determined from application of the Square Law:
Equation 13 – Series-Parallel Fan Pressure:
2
Pfan = R ED × Q fan
Using an initial quantity, and the resistance values determined from the previous formulae,
the airflow and pressures throughout the network are evaluated directly without iteration.
3.2.2.3 Resistance of Leakage Paths
Leakage is quantified in DuctSIM using the unit of resistance of leakage per 100 m of duct.
The following relationship (Woronin’s Equation, Vutukuri, 1986) may be used to help
quantify this parameter from measured data for existing duct installations. In this case Rl is
DuctSIM Design Manual – Version 1.0b – October 2003
12
the leakage path resistance per 100 m long duct, Q1 is the upstream quantity and Q2 is the
downstream quantity.
Equation 14 – Woronin’s Equation: R l =
 L 
Rd ×

 100 
3
  Q1  
3× 
- 1 


Q
2

 
2
The following formula (Browning, 1983) may be used to estimate the term Rd from measured
data. It is necessary to use such an approach, which uses a weighted mean quantity, because
the leakage along the duct is continuous and varying. The Square Law (Equation 5) should
only be used to evaluate airway resistance when the quantity term is reasonably constant
along the entire measurement section.

(P - P ) 
5
Equation 15 – Browning’s Formula: R d = 1 2 

L
 2Q 1 + 3Q 2 
2
The leakage resistance is extremely sensitive to duct airflow leakage, such that a relatively
small deterioration in a duct will result in an order of magnitude drop in the leakage
resistance. In this sense the leakage resistance is a difficult parameter to measure, and it is
also a difficult task to allocate an appropriate value to both proposed and existing duct
installations. The leakage from ducts is affected by the ducting material, quality of
installation, number of joints, total length, pressure difference between the inside and outside
of the ducting and the duct diameter. To assist with the user in selecting a suitable leakage
resistance, a series of typical design values have been provided in Table 2. These values have
been computed from actual airflow and pressure measurements taken for different duct
installations.
The leakage slider in DuctSIM provides a leakage resistance range of 100 to 150,000 Ns2/m8
(962.5 to 1,443,750 P.U.). The upper limit represents an extremely good duct installation. It
is recommended that the user enter realistic values for the duct leakage, to avoid design
errors.
Leakage Condition
Rigid Duct
Excellent Condition
Good Condition
Poor Condition
Bad Condition
Flexible Duct
Excellent TBM Cassette
Duct
Typical Mine Duct
Poor Condition
Resistance of Leakage Paths Resistance of Leakage Paths
per 100m duct (Ns2/m8)
per 100ft duct (P.U.)
150,000
120,000
40,000
1,000
1,443,750
1,155,000
385,000
9,625
50,000
1,500
100
481,250
14,438
962.5
Table 2: Typical Leakage Resistance per 100 m or 100 ft of Duct
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3.2.3
Zones
The Zones sheet (see Figure 3) allows the user to split the duct into one or more zones, each
of which may have different physical characteristics. The data are entered into a table that has
columns for the start distance, end distance, duct diameter, Atkinson friction factor and
leakage resistance. The DuctSIM program will adjust these lengths to fit them to the closest
leakage path. The software internally assigns 99 evenly spaced leakage paths to the duct,
which results in 100 identical segments. Hence, the largest correction made to a length will
be half of a segment, or about 1/200th of the total duct length. This process is illustrated in
Figure 9, which shows a two-part duct installation. The first section is spiral wound steel duct
that transitions into smaller flexible force bag. It can be seen that the transition point does not
correspond exactly to a leakage point, hence both the end point of Zone 1 and the start point
of Zone 2 are automatically adjusted by the DuctSIM program.
Duct
Duct Length/100
Leakage
Path 1
Leakage
Path 99
Drift or Tunnel
Fit transition
ZONE 1
Start Zone 1
Face
ZONE 2
End Zone 1
Start Zone 2
Spiral Wound Steel Duct
Flexible Force Duct/Bag
Actual transition
Figure 9: Explanation of the Zones Concept
It is important that the user enter sufficient zone information to describe the full length of the
duct. The zones must connect together to form a continuous description of the duct from the
start through to the end. The user may also chose whether to apply or ignore the zone
information, by tagging zones on or off.
The zones page also has a tag that allows the user to automatically include the transition
shock losses associated with changes in area along the duct. The program determines whether
the transition will be a contraction or expansion, which is dependent on the relative area of
adjacent zones and the direction of airflow (whether it is forcing or exhausting). The
transition is assumed to be abrupt. If the user requires a gradual transition, then the shock loss
resistance should be manually calculated and entered. Refer to Section 3.3 and Table 3 for
details on shock losses.
For typical duct applications the zones feature will generally not be used. This adds a level of
complexity to the analysis and is not recommended unless the duct has sections with a
significant change in diameter, friction factor or leakage.
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3.2.4
General
The general page (see Figure 3) allows the user to enter an average air density, and also to
select whether the duct is forcing or exhausting air.
The duct air density is used during the fan calculation procedure. A correction is
automatically made to each fan characteristic curve based on the relationship between the air
density for the fan curve (typically provided at standard/sea level = 1.2 kg/m3) and the duct
air density. This conversion process is described in Section 3.4.
The user is required to specify whether the duct is forcing or exhausting to ensure that duct
shock losses are correctly calculated, and to provide the correct graphical trends. It should be
noted that the leakage values of the duct are not automatically adjusted when the user
switches from a forcing to an exhausting system. In practice it is likely that the leakage
resistance associated with an exhausting duct (that is predominantly under a negative
pressure) will be higher than a forcing system, due to the joints being sealed better. If
required the user will need to manually enter any changes in the leakage resistance value.
In addition, this page allows the user to change the default runtime parameters for the
software. DuctSIM has a default mode of execution termed “Normal,” with the option of
selecting either “Quick” or “Detailed” as other choices. This basically adjusts the accuracy of
closure for the iterative solution used for the Hardy Cross technique. The “Quick” mode
provides for an absolute closure in any branch less than 0.01 m3/s (21 cfm), “Normal” closes
to within 0.001 m3/s (2.1 cfm), whereas “Detailed” requires a closure of less than 0.00001
m3/s (.02 cfm) for all branches. According to the particular duct problem the user may wish to
change the default execution mode, either to accelerate the speed of execution for draft runs,
or conversely to obtain the most accurate results. The user may also change the limit for the
number of executions. This is preset to 5,000, after which the Hardy Cross solution will stop,
and the results for the last iteration will be printed. For some cases, especially in long ducts
with high leakage, and when the user has selected “Detailed” for the accuracy, the user may
need to increase the iteration limit.
For normal duct design the user should not need to change either the iteration limit or the
mode of execution.
3.2.4.1 Forcing Versus Exhausting Duct Systems
Forcing ventilation provides positive airflow to the face. The air leaves the end of the duct
with momentum, and hence will be thrown down the drift towards the face. This effect assists
with mixing and flushing strata and exhaust gases from the face areas and provides a degree
of convective cooling to any workers in the area. Furthermore, the fan and motor are always
in the fresh air. The main disadvantage with this approach is that the entire tunnel is
exhausting contaminated air from the face. This can make unpleasant and unhealthy work
conditions and can delay re-entry times following blasting. A typical forcing system is shown
in Figure 10.
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Face
Return Air
Forcing Duct - Intake Air
Fan
Figure 10: Typical Force Ventilation System
Exhausting ventilation is an option that allows the entire tunnel area to be kept clear.
Furthermore, the contaminated air in the duct can be filtered prior to discharging. A typical
exhausting duct system is shown in the following figure.
Dust/Gas/Smoke
Face
Intake Air
Exhausting Duct - Return Air
Fan
Figure 11: Typical Exhaust Ventilation System
The disadvantage with exhaust ventilation is a low face quantity that requires that the duct be
kept close to the working face (less than 3 m [10 ft] for effective air movement). This is
illustrated in Figure 12.
An exhausting duct inlet is shown, with contours showing the percentage of the duct air
velocity as one progresses further from the inlet. For example, at a distance of 0.5 × duct
diameter, in a direction inline with the duct, the velocity is about 30 % of that in the duct.
A refinement for the exhaust case is the exhausting duct with a force-overlap system (also
know as a “scavenger” system). In this case the exhaust duct is taken to a point about 30 m
(100 ft) from the face. A smaller diameter forcing duct picks up approximately 10 m (33 ft)
from the intake of the exhaust duct and delivers the air to the face. The disadvantages of this
configuration include:
1. The quality of the air delivered to the face is typical inferior to force system. The slow
moving air can pick up heat, dust and gases while moving along the tunnel or drift.
2. Two ventilation ducts and fans are required.
DuctSIM Design Manual – Version 1.0b – October 2003
16
d
0
90 %
60 %
0.5 d
30 %
15 %
7.5 %
1.0 d
Figure 12: Reduction in Air Velocity with Distance - Exhaust Duct (after Black et al., 1978)
3. Electrical utilities have to be maintained throughout the heading and close to the face.
4. Poor conditions can result in the overlap transition.
5. Care needs to be taken to avoid recirculation in the exhaust duct if multiple fans are
staged along the duct.
6. Clearance for equipment is required at the overlap due to the presence of two ducts in
the drift or tunnel.
A typical exhausting duct with a force-overlap is shown in Figure 13.
Forcing Fan and Duct
Face
Intake Air
Exhausting Duct - Return Air
Fan
Overlap
Figure 13: Typical Exhaust Duct with Force Overlap
The final option is the forcing duct with an exhaust overlap. An example of this configuration
is shown in Figure 14. In this case the advantages of a forcing system are achieved, in that the
duct can be flexible, chillers can be used to directly cool the face close to the working area,
and a high discharge velocity can be used to flush the face. The exhaust scavenger duct
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17
allows a portion of the face air to be filtered, which assists in maintaining acceptable air
quality conditions along the length of the tunnel.
Exhaust Duct with Filter
Face
Return Air
Forcing Duct - Intake Air
Fan
Figure 14: Typical Forcing Duct with Exhaust Scavenger
3.2.5
Input Data Ranges
The following ranges must be adhered to during data entry with the DuctSIM program:
3.3
•
•
•
•
Diameter
Length
Atkinson friction factor
Resistance of leakage paths/100m(100ft)
•
Air density
- 0.1 to 20 m (0.33 to 65.61 ft)
- 10 to 100,000 m (33 to 328000 ft)
- 0 to 1 kg/m3 (0 to 5390 x10-10 lbf min2/ft4)
-100 to 150,000 Ns2/m8 (962.5 to
1,443,750 P.U.)
- 0.1 to 2 kg/m3 (0.00624 to 0.1249 lb/ft3)
Shock Loss Details
When obstructions occur within a duct, the airflow is retarded in two ways. First the
obstruction causes a reduction in the free cross-sectional area, and second the flow pattern of
the air is disrupted. For example, significant energy losses can occur when air enters a duct,
due to the air being accelerated from a stagnant condition to the velocity within the duct. The
amount of energy lost depends on the shape of the entrance. Similarly, when air flows
through an orifice the air enters from all directions on the high-pressure side, but is
discharged as a jet on the low-pressure side. Again significant losses result.
The DuctSIM program allows information to be input to incorporate shock losses in the duct
(Figure 15).
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Figure 15: Shock Loss Data Dialog Box
DuctSIM Design Manual – Version 1.0b – October 2003
19
These losses include:
•
•
•
Entry losses
Exit losses
Smooth elbow
•
•
•
•
Mitred elbow
Dampers
Screen
Fixed Resistance
- sharp, flanged or formed bell
- abrupt, flanged or diffuser
- Radius/diameter: 0.5, 0.75, 1.0, 1.5, 2.0, 2.5
- Angles: 45°, 90°, 135°, 180°
- Angles: 45°, 60°, 90°
- Degrees closed: Wide open, 10°, 20°, 30°, 40°, 50°, 60°
The shock loss factor (C) is determined for each type of obstruction based on ASHRAE
(1989) fitting data. The user can input up to 20 instances of each obstruction by entering the
length along the duct at which the fitting is installed. Pressing the Calculate button will show
the results immediately; however the program will automatically conduct all required
calculations once the dialog box is closed. The Clear Form button clears the shock loss input
sheet.
In addition to these losses, the user may also select to have the program automatically
compute and include the expansion or contraction shock loss associated with the air moving
between two sections of duct with dissimilar areas. The tag for this feature is contained in the
zones page (Section 3.2.3). The program determines whether the transition will be a
contraction or expansion, which is dependent on the relative area of adjacent zones and the
direction of airflow (whether it is forcing or exhausting). The transition is assumed to be
abrupt. If the user requires a gradual transition, then the shock loss resistance should be
manually calculated and entered as a fixed resistance.
3.3.1
Shock Loss Theory
Shock losses, also called dynamic losses are typically referred to in terms of velocity
pressure. A shock loss factor, or loss coefficient is the number of velocity pressures
associated with the shock loss.
The following formulae are used to evaluate velocity pressure (Equation 16), pressure loss
associated with the shock loss (Equation 17) and the equivalent resistance of the shock loss
(Equation 18).
ρ u2
2
Equation 16 – Velocity Pressure:
pv =
Equation 17 – Shock Loss Pressure:
p shock = C p v
Equation 18 – Shock Loss Resistance:
R shock =
p shock
Cρ
=
2
2 A2
Q
Table 3 provides a list of the various shock loss coefficients incorporated in the DuctSIM
program.
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Description
Illustration
Conditions
Loss
Coeff.
Entry Losses
Sharp
Aamb
Aduct
1.00
Aamb
Aduct
Flanged
Aamb is
infinite
0.50
Aamb
Formed
Bell
Aduct
0.10
Exit Losses
Abrupt
Aamb
Aduct
Aamb is
infinite
1.00
Aamb
Flanged
Aduct
0.88
Aduct
0.51
Aamb
Diffuser
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21
Smooth Elbow
45 Degrees
θ
45
r/D
0.50
0.75
1.00
1.50
2.00
2.50
r/D
0.50
0.75
1.00
1.50
2.00
2.50
r/D
0.50
0.75
1.00
1.50
2.00
2.50
r/D
0.50
0.75
1.00
1.50
2.00
2.50
θ
90
90 Degrees
Aduct
θ
135
135 Degrees
θ
D
θ
180
180 Degrees
Mitre Elbow
θ
θ
45
60
90
0.40
0.20
0.13
0.09
0.08
0.08
0.71
0.33
0.22
0.15
0.13
0.12
0.85
0.40
0.26
0.18
0.16
0.14
0.99
0.46
0.31
0.21
0.18
0.16
0.34
0.55
1.20
Aduct
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22
Damper
(with the
same
diameter as
the duct)
θ
Wide Open
10
20
30
40
50
60
Free area
ratio screen
= 0.6
θ
Aduct
Screen
Screen
Screen
Diameter =
Duct
Diameter
Aduct
0.19
0.67
1.80
4.40
11.0
32.0
113
0.97
Abrupt
Expansion
A1
A2
A

C 2 =  2 - 1
 A1 
2
Abrupt
Contraction
A1
A2
 A 
C 2 = 0.5 1 - 2 
 A1 
2
Table 3: Shock Loss Coefficients Incorporated in the DuctSIM Program (after ASHRAE,
1989)
The fixed resistance input feature should be used if a particular shock loss is not included in
the table, or if the loss is different than that provided. An example of this may be the
inclusion of a screen that has a free area ratio that is not 0.6, or a butterfly damper that has a
diameter less than that of the duct. For cases such as these the user is advised to manually
compute a shock loss resistance from a suitable reference (such as ASHRAE, 1989) and enter
this directly in the fixed resistance page.
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3.4
3.4.1
Fans
General Details
Fans in mining and tunnelling applications may be broadly categorized as either centrifugal
or axial-flow fans. The flow through a centrifugal fan is mainly radial in the region of energy
transfer. The fan impellor resembles a paddle-wheel, in which the air enters near the centre of
the wheel. Centrifugal fans may have either radial, backward curved or forward curved blade
design. The highest efficiencies are often associated with backward curved blades, which
generally provide the greatest operating pressure for a given rotor size.
A vane axial (axial-flow) fan relies on the same principal as an aircraft propeller. The
direction of flow through a vane-axial fan is predominantly parallel to the axis of rotation,
with ideally little or no velocity component in the radial direction. Axial fans generally rotate
at a higher blade tip speed than centrifugal fans of similar performance and therefore they are
often noisier. These fans also suffer from a definite stall characteristic at high resistance,
which is not the case with centrifugal fans. However, vane axial fans are more compact, and
can be designed to be reversible. Vane axial fans are generally the fan of choice for auxiliary
duct installations. They are lightweight, and can be mounted inline with the duct with little or
no additional obstruction.
3.4.1.1 Auxiliary Fan Installation Guidelines
Table 4 shows a series of typical auxiliary fan installations, and identifies the correct and
incorrect configuration for each case. This table should be used to help optimise and plan the
installation of vane axial fans in duct systems.
3.4.2
Inputting Fans in the DuctSIM Program
The user may allocate fans to the project from any view. A fan may be added, edited or
deleted from the duct by selecting the appropriate option under the Fans Menu, or by pressing
the “+”, “-“ or “E” buttons that correspond to add fan, delete fan or edit fan. The fan
information may be summarized and viewed in the Fan Input View, which contains a tabular
list of all fans. An example for the Fan Input View is shown in Figure 16. Summarized are
the main fan details including the manufacturer, model, setting, distance along the curve, air
density for the fan curve, fixed fan pressure (if applicable), and tags stating whether a fixed
pressure is being applied and whether the user has entered a curve for the fan. DuctSIM
provides a fan sort routine in the Fan Input View. This allows the user to sort the fans in order
of increasing distance, and is activated by selecting Sort Fans under the Tools Menu.
Figure 16: Fan Input View
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RECOMMENDED
A flanged inlet starves the
impellor blade tips of air
reducing performance and
increasing noise.
A bell-mouth inlet guides
air into the impellor blade
tips.
Avoid obstructions
close to fan inlet. Part
of the impellor is
starved of air.
Allow a
space of at
least 1
diameter at
the fan
inlet.
Avoid obstructions
close to the fan outlet.
Allow a space
of at least 1
diameter at
the fan outlet.
Avoid fan terminating the
discharge end of the
system.
Fit a duct length of
at least 2
diameters or an
outlet expander
(1.26 diameters)
after the discharge
end of the fan.
Flexible connectors
should not be slack as
this will cause
"necking", which will
starve the impellor
blade tips of air, reduce
fan performance, and
increase noise.
d
d
d
d
2d
Use a square
bend with short
chord turning
vanes. This is
also preferable
when airflow is
in the opposite
direction.
Fan performance
suffers and noise is
increased if a 90
degree circular bend
of small radius is
used.
Do not use an
expander of 30
degrees or more
immediately before
or after a fan.
d
1.26d
WRONG
Ideally an expander
immediately before a fan
should not be more than 15
degrees.
α
α
Flexible connectors should
be just long enough for
mechanical isolation and
should be taught.
Connectors
Connectors
Table 4: Auxiliary fan Installation Guidelines (after JM Aerofoil Fans, 1999)
When the user selects to add a new fan, or decides to edit an existing fan, the Add Fan dialog
box is shown (see Figure 17).
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25
Figure 17: Add Fan Dialog Box
This dialog box prompts the user to enter the following information:
•
•
•
•
Distance along the duct measured from the non-face side
A fixed fan pressure (optional).
A fan curve (optional).
If a fan curve has been entered, then the fan manufacturer, model, blade setting, fan
curve density and the number of fan curve points will be listed.
The user may enter a fan curve directly by pressing the Edit Fan Curve button or may import
a curve from an existing fan database using the Import Fan Curve button. If the user tags to
use the fixed pressure, then a value must be entered in the fixed pressure cell. Similarly, if the
user does not tag to use fixed pressure, then a fan curve must be included.
3.4.3
Fan Curves
If the user elects to input a fan curve, then the dialog box shown in Figure 18 is shown. The
user has the choice of entering descriptive data for the:
•
•
•
Fan manufacturer
Fan model
Fan blade setting
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Figure 18: Fan Curve Dialog Box
The user must enter the air density, which represents the density at which the curve was
developed (typically at standard air density = 1.2 kg/m3 [0.075 lb/ft3]). The fan characteristic
curve must then be entered. The following rules should be adopted when entering fan curve
information:
•
•
•
•
•
Enter at least two data points and less than 15.
Pressure and quantity data must be entered for each point. If available, efficiency data
should also be added. If efficiency data are not included then the fan power
calculations and results will be disabled.
All pressure values should be entered as fan total pressure (see Section 3.4.3.2).
The points should be chosen such that they adequately represent the full extent of the
curve.
The user may enter the points in any order. The program will automatically conduct a
full sort and data validation when the dialog box is closed. When the user next looks
at the curve it will have been sorted in order of descending pressure/ascending
quantity.
A fan curve is a graphical depiction of the pressure-quantity characteristic associated with a
certain fan and configuration. This pressure-quantity characteristic will vary according to a
number of factors. For vane-axial fans, the fan blade angle may be adjusted, or the speed of
the blade rotation may be changed. For centrifugal fans, which have a fixed impellor, the
characteristic may be changed by adjusting the rotational speed of the impellor, or by
adjusting the flow path taken by the fan as it enters the impellor (inlet vane controllers).
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Figure 19 shows a set of example curves for a vane axial fan. This fan has three distinct blade
settings termed #1, #2 and #3. The fan total pressure is provided on the primary y-axis, with
the fan brake horsepower on the secondary y-axis. The fan quantity is on the x-axis. The
relationship termed the system or duct equivalent resistance is shown, which plots pressure
loss against quantity for the equivalent duct resistance “seen” by the fan. This trend is
evaluated from the Square Law (Equation 5). This duct resistance curve intercepts the fan
curve at the fan operating point. The total pressure and quantity are read directly from this
point. The brake horsepower for the fan is obtained by dropping a line down from the
pressure-quantity curve to the correct horsepower curve. The fan brake horsepower is then
read off the secondary y-axis as shown in Figure 19.
3.0
#3
Pressure-Quantity
Curves
Duct/System
Resistance
#2
#1
2.0
Fan Operating
Point
1.5
60
#3
50
#2
#1
1.0
40
Pressure-QuantityPower Curves
30
0.5
20
Brake Power (kW)
Fan Total Pressure (kPa)
2.5
10
0.0
0
0
5
10
15
Quantity (m3/s)
20
25
30
Figure 19: Example Fan Curve
When solving fan curves, the DuctSIM program assumes a linear relationship between any
two points on the fan curve. If the operating point lies to the left of the user-defined curve,
then a constant pressure is assumed at the peak pressure (input by the user). If the operating
point lies to the right of the user-defined curve, then the curve is interpolated based on the
slope of the last two points (even into the negative pressure quadrant).
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Figure 20 illustrates the selection of points for DuctSIM. In this case 8 characteristic points
have been plotted on the red fan curve. The DuctSIM program will fit straight lines between
each of these 8 points as shown by the black connecting lines. At the top of the curve (left
side) interpolation is at constant pressure based on point 1. At the bottom of the curve (right)
interpolation is based on the slope of the last points, which are 7 and 8. The shaded area
represents the region formed between the minimum and maximum pressures and quantities
for points 1 to 8. Any operating point falling in this range is deemed as being “on” the curve.
Interpolated at Constant
Pressure
1
2
3
Fan Points
4
Pressure
5
Area formed within pressure
and quantity range classified
as being "ON" the curve
6
7
8
Interpolated
at Slope of
Points 7-8
Quantity
Figure 20: Fan Curve Showing Selection of Points and Interpolation
3.4.3.1 Fan Stall
Aerodynamic stall occurs with vane-axial fans when the fan blade angle of attack is greater
than the angle of maximum lift, which results in the breakaway of the boundary layer (air) on
the upper surface of the fan blade. The end result is a loss of lift and additional drag. An
increase in the system resistance is usually required to force a fan into this operating mode,
whereby the resistance reaches a critical value after which the fan is functioning beyond the
normal operating range. When a fan is running in stall condition it will start to vibrate
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excessively and produce low-frequency noise. This noise is often obvious, however if a fan is
slowly driven into the stall zone then an abrupt transition may not be recognized. A fan
should never be allowed to run continuously in this condition, which can result in the failure
of the blades and excessive wear in other critical components. Such a situation represents
both a potential safety and maintenance problem.
In large-scale applications, it is common that controls are placed on the mine fans to alert
personnel when the fan operating pressure rises beyond a certain point. At this stage the
personnel are required to either lower the system resistance, or adjust the fan curve (change
the blade angle, or if available, the speed of the fan). On smaller auxiliary fans this degree of
monitoring is usually not required, and the peak operating point is typically predetermined in
the form of a maximum length of duct-line attached to the fan. It is then a matter of
developing and implementing procedures to ensure that the fan is never required to operate
with duct exceeding this maximum length. In addition to the duct length, there are other
factors that should be considered in auxiliary duct installations. These include the diameter
and type of duct (flexible or rigid), the condition of the duct, and the shock losses associated
with the installation (bends, expansion, contraction, etc.). Hence, it is also important that a
consistent plan be adopted regarding the type and diameter of duct, and the layout of the
overall auxiliary ventilation system to minimize losses at bends.
3.4.3.2 Pressure Gradients
The DuctSIM program requires that fan curves be entered in terms of total pressure, where:
Equation 19 – Total Pressure:
Total Pressure = Static Pressure + Velocity Pressure
Velocity pressure is the kinetic energy applied to the motion of the air through the duct. Static
pressure is not related to the air motion, and exerts a force in all directions, much like the air
pressure inside a balloon. Figure 21 shows an example of the pressure profiles existing along
a duct. In this case the duct has a single fan, with a transition between two different duct
sizes.
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Large Duct
Fan
Small Duct
5
5
4
Fan Velocity Pressure
3
Fan Total Pressure
2
1
-1
Fan Static Pressure
3
0
4
Datum - Outside Duct
Duct T
otal P
ressure
Large
Duct V
elocity
Press
ure
Sm
Ve all D
Pre locity uct
Du
ssu
ct
re
Sta
tic
Pre
ssu
re
2
1
0
Discharge
Velocity
Pressure
-1
-2
-2
-3
-3
Figure 21: Typical Pressure Profiles Along a Duct
The relationships of duct pressures to the plotted profile are as follows:
1. The duct total pressure is always zero (with respect to the datum – surrounding drift
or entry) at the entrance to the duct. The duct static pressure at the entrance is always
negative at the entrance and is equal to the duct velocity pressure at that point.
2. The duct total pressure is always positive at the discharge to atmosphere and is equal
to the duct velocity pressure at that point. The duct static pressure at discharge is
always zero.
3. The fan total pressure is the difference in duct total pressure across the fan.
4. The fan static pressure is the difference between the duct total pressure at the inlet and
the duct static pressure at the outlet. Hence, the fan velocity pressure is taken on the
outlet side of the fan.
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3.4.4
Fan Laws
When selecting a suitable fan, care must be taken to convert correctly between the fan total
pressure and fan static pressure. Some manufacturer’s curves are provided as total pressure,
whereas others provide the fan static pressure and require the fan velocity pressure to be
calculated to accurately account for any fixtures associated with the fan.
Fan Laws are a particular version of the general similarity laws that apply to all classes of
turbo-machinery. They express the relationships various performance variables, including:
1.
2.
3.
4.
5.
6.
Fan impellor size
Fan speed
Fan air density
Fan flow rate
Fan total pressure
Fan Air Power
– d (m [ft])
– N (rpm)
– ρ (kg/m3 [lb/ft3])
– Q (m3/s [cfm])
– p (Pa [in.w.g.)
– Pow (W [hp])
In practical utilization or design of fans we are normally interested in varying only one of the
independent variables of speed, air density or impellor size at any one time. The fan laws may
therefore be summarized as:
Fan Speed (N)
P ∝ N2
Q∝N
Pow ∝ N3
Impellor Diameter (d)
p ∝ d2
Q ∝ d3
Pow ∝ d5
Air Density (ρ)
P∝ρ
Q fixed
Pow ∝ ρ
Table 5: Fan Laws
A correction is made in the DuctSIM program for the difference between the actual duct air
density at which the fan is operating, and the air density for which the fan curve was
developed. Since quantity is independent of pressure, and pressure is directly proportional to
pressure, the following formula is used to correct the fan pressures:
Equation 20 – Fan Pressure Adjustment:
Pa = Ps
ρa
ρs
Hence, as the duct air density increases the fan pressure required to move the same volume of
air increases. This is sensible since a unit volume of air will now be heavier, which will
require that the fan do more work to move it.
3.4.5
Fan Database
DuctSIM incorporates a data archival tool for the development, manipulation and storage of
fan curves. This feature is called the fan database. The fan database allows the user to
generate different fan files, each of which can hold many different curves. Hence, the user
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may select to have just one database file for all fans, or conversely, have a separate database
file for each fan, perhaps with the different curve settings saved.
The fan database is accessed directly from DuctSIM by selecting File/Open and choosing the
fan database file (*.fdb extension). The user may develop a new fan database file by selecting
File/New and choosing Fan File as the new file type (not DuctSIM).
An example of the Fan Database View is shown in Figure 22. The user can add, edit or
remove fans from the particular database file by either using the Fans Menu, or the toolbar
buttons (“+”, “E” and “-“). When adding or editing fans the dialog box shown in Figure 17
will be shown. As the fans are added the pressure and quantity points are sorted and validated
(to ensure that the data is sensible).
Figure 22: Fan Database View
It is important to understand the difference between fans saved in the fan database files and
the DuctSIM files. The DuctSIM file saves the fan information for all of the fans that have
been allocated to one particular duct. The fan database file is a source that the user may pull
fan data from to add to any DuctSIM project. A specific fan characteristic curve is added to
the DuctSIM project by selecting the Import Fan Curve feature shown in Figure 17. At this
point the user is allowed to browse for fan database files (locally or throughout a network).
When a fan database file is selected the Select Fan dialog box will appear (Figure 23), which
shows all of the fan curves contained in that database. The user can then select a fan to add to
the project.
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Figure 23: Select Fan to Add to Project Dialog Box
3.4.6
Fixed Pressure Fans
The user may select not to use a fan curve and enter a fixed pressure for one or more fans in
the duct. This will allocate a specific operating pressure to the fan that will not change, even
if the duct resistance is adjusted. Fixed pressure fans are often used when the user has taken
measurements for an existing duct and is attempting to simulate that duct using the program.
In this case it can be helpful to fix the fan pressure at the measured pressures, and then
examine the predicted and measured airflows to evaluate the accuracy of the model. Another
use for fixed pressure fans is early in a duct design project, prior to the selection of a suitable
fan, when the fixed pressure option is used to help estimate the approximate fan size and
spacing (usually by iteration).
If the fixed pressure option is used then all efficiency data will be omitted from the
simulation, and fan input power values will not be provided. Efficiency data are only
included when fan curves are used in the model.
3.5
Input View
The information input to describe the duct and fan(s) is summarized in the Input View. This
view is shown in Figure 24. The following data are provided:
•
•
•
•
Physical Data – Duct diameter and length.
Fan Data – Total number of fans, number of fans operating on a curve, the number of
fixed pressure fans and whether the duct is forcing or exhausting air.
Resistance Data – Atkinson friction factor, number of leakage paths (preset to 99) and
the resistance of the leakage paths per 100m of duct.
The start point, end point, diameter, Atkinson friction factor and resistance of leakage
paths for all zones allocated in the project.
After entering the various input parameters, the user is advised to closely examine the Input
View to ensure that the data is sensible.
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Figure 24: Input View
3.6
Fixed Quantity Tool
DuctSIM contains a feature called the Fixed Quantity Tool. This tool allows the user to
conduct the following calculations:
1. Determine the fan total pressure and quantity for a specified airflow requirement at
the working face.
2. Determine the face airflow and fan total pressure for a specified fan quantity.
In both cases it is assumed that the fan is remote from the face (at the other end of the duct,
per Figure 10). Furthermore, all fans are ignored if the user elects to use this tool. DuctSIM
makes use of the Series-Parallel Method to solve the fixed quantity problem, rather than the
Hardy Cross Iterative Technique that is used when fans are present (see Section 3.2.2). The
fans are removed from the simulation due to the potential conflict of having allocated fixed
quantities and non-compatible fans in close proximity in a duct system. In this case problems
such as excessive required pressure, or fans forced to operate far off their designated curve
can result.
Figure 25 shows the dialog box used to input the fixed quantity data.
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Figure 25: Fixed Quantity Tool Dialog Box
The Fixed Quantity Tool is generally used to determine the fan requirement for simple onefan duct installations, or to help determine an approximate fan power requirement for a
proposed duct system. The results from the computation are the predicted face and fan
quantities, and the required fan pressure. This information is provided in the Results View.
3.7
Notepad
The DuctSIM program has a notepad that allows the user to enter descriptive data about the
particular modelling scenario. The notepad dialog is accessed under the Tools Menu. This
dialog box is shown in Figure 26. The text contents of the notepad are saved as part of the
DuctSIM file, however these contents are not printed under any of the views.
Figure 26: Notepad
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4
VIEWING THE RESULTS
Following the input of all required data, the user conducts the simulation by either selecting
Tools/Execute from the menu, or by pressing the Execute button. This simulation is also
conducted automatically whenever an existing file is opened. If there is an error associated
with the input data a message box will be posted stating the exact nature of that error. If there
is no error box then the simulation has been executed successfully. All views are updated
automatically.
Four main views are used to present the output for the DuctSIM program. These are the
Results View (provides a summary of the important data obtained from the simulation), the
Fan Results View (tabular view that lists details about each fan), the Fan Curve View
(graphical plot of the fan curve with listing of operating data) and the Graph View (plots
trends of flow and pressure against length and shows a schematic of the duct).
4.1
Results View
The Results View provides a summary of the main results (see Figure 27). The following
information is provided:
•
•
•
•
4.2
General Data – Duct area, perimeter, length of each duct segment (total length/100),
number of meshes (preset to 100), and the number of iterations if the Hardy Cross
technique is used.
Resistance Data – Total duct resistance, resistance per segment of the duct (1/100th of
the total resistance), resistance of each leakage path, and the total shock loss
coefficient
Fan or Fixed Quantity Data – The quantity of air in the first and last duct segments,
whether the simulation is a fixed quantity run or a fan simulation, and if the execution
is for a fixed quantity, the fan pressure required.
If zones are included, the duct area, perimeter, resistance per duct segment and
resistance of each leakage path are provided for each zone.
Fan Results View
The Fan Results View provides a tabular list of the fans and predicted operating points (see
Figure 28). The following data are listed in the table:
•
•
•
•
•
•
•
•
Distance of the fan along the duct
Descriptive data about the fan
Fan total pressure
Fan quantity
Fan efficiency
Air power = fan pressure × fan quantity
Fan input power = air power/fan efficiency
A tag stating whether the fan is operating on or off the fan curve.
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Figure 27: Results View
The fan is off the curve if the operating point falls outside of the range defined by the input
points. The operating point may be off the left side of the curve, which suggests that the
system resistance is too high, or off the right side, which suggests that the fan is too small for
the application (see Figure 20). If a fixed pressure is specified, then “NA” appears in the
efficiency, input power and on-curve columns for that fan.
Figure 28: Fan Results View
4.3
Fan Curve View
The Fan Curve View shows the operating characteristics for each fan in the project. The data
are presented in a split view that consists of:
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1. A form view on the left that lists the fan descriptive data, air density, and the fan
operating characteristics (pressure, quantity, efficiency and power). This sheet has
two drop-down lists that enable the user to toggle through fans and select what data to
plot.
2. A graph view on the right plots the fan-operating curve. The user also has the option
of overlaying the input fan power/horsepower for each data point on the curve. These
data points should be read off the secondary y-axis. The fan operating point for
pressure, quantity and power is indicated using red construction lines.
This view provides a visual perspective of the operating characteristic for each system fan.
The experienced user will be able to identify such factors as:
•
•
•
Fans operating close to, or in a stall condition
Fans that are of an incorrect size
Inefficient operation
Figure 29: Fan Curve View
4.4
Graph View
The Graph View allows the user to plot airflow and pressure trends against duct length. Also
included is a schematic of the duct showing the location and type of shock losses and fans,
and the direction of airflow. The user can tag which trends to plot on the graph, and which
information to draw on the schematic using the Graph Trends dialog box (see Figure 30).
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Figure 30: Graph Preferences Dialog Box
For the airflow trend the user may select whether to plot the quantity in the duct or the air
velocity. For the pressure trend the user may select the duct total and/or static pressure. The
difference between these trends at any point along the duct represents the duct velocity
pressure. Detailed information relating to duct pressure profiles is provided in Section
3.4.3.2, and is shown on Figure 21.
Figure 31 shows a typical plot in the Graph View. The upper region of the screen shows the
actual graph, with the lower area showing the duct schematic. In this case the graph is
showing plots of the duct static and total pressures (primary y axis) and the duct air velocity
(secondary y axis). The total pressure trend is shown by the continuous blue line, the static
pressure by the continuous green line, and the velocity trend by the dashed red line. The zeropressure line is denoted by a dashed blue line. The schematic shows that there are two fans in
the duct, and that the duct is a forcing system. The duct entry configuration is a bell mouth,
with a diffuser at the exit. There are two shock losses shown, with codes of SE and D. The
following shock loss codes are used in the schematic:
•
•
•
•
•
SE
ME
D
S
FR
- Smooth Elbow
- Mitre Elbow
- Damper
- Screen
- Fixed Resistance
There is a sudden pressure peak across each fan that can result in negative pressures on the
inlet side and a large positive pressure on the discharge. For the case shown in Figure 31 the
duct is maintained on positive pressure. If the pressure trends become negative on the inlet
side of the fans, and flexible duct is being used, then the fans have to be resized or the
spacing changed. If the duct were rigid with negative pressure zones, then recirculation
would occur along the duct. The pressure loss associated with the damper can also be seen in
the pressure trend, where a step change occurs. This is not the case with the smooth elbow
DuctSIM Design Manual – Version 1.0b – October 2003
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shock loss, which has a much lower resistance, and smaller pressure loss associated with it.
The step change in the velocity is due to there being two discrete zones for this duct, each
with a different area. See Section 3.2.3 for a detailed description of the zones concept.
Figure 31: Graph View
The Graph View is generally the primary method of examining the results for each
simulation. Using an iterative approach of moving and changing fans the duct system can be
rapidly optimised to achieve face airflow requirements, and to minimize or avoid negative
duct pressures or recirculation.
4.5
Printing
Printing of input and output data is conducted on a view-by-view basis by selecting Print
Preview or Print. The printer font is preset to ensure legibility of the output. For the tabular
views it is recommended that the Print Set-up be tagged for landscape orientation, and that
the columns be resized (and hidden if necessary) to ensure that the pertinent information fits
on a single sheet.
The Fan Input and Fan Results views are not printed as tables (as shown on the screen). The
print output from the Fan Input view provides descriptive fan information, distance along the
duct, and a listing of the input fan curve. A sample of this print output is shown in Figure 32.
The Fan Curve View does not have a Print or Print Preview option. The fan curves are
instead printed from the Fan Results View. The printout in this view contains information on
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a fan-by-fan basis (similar to the Fan Input View). A sample of this print output is shown in
Figure 33.
Figure 32: Print Preview from the Fan Input View
Figure 33: Print Preview from the Fan Results View
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5
REFERENCES
ASHRAE Handbook, 1989, “Fundamentals,” I-P Edition, Published by the American
Society of Heating, Refrigeration and Air Conditioning, Inc., pp. 32.27 – 32.52.
Black S. and Banerjee B., 1978, “Effect of Continuous Miners on the Generation of
Respirable Dust,” Mining Congress Journal, March 1978, pp. 19-25.
Browning E.J., 1983, "An Approximate Method for Auxiliary Ventilation Simulations,"
The Mining Engineer, September, pp. 129 - 134.
Calizaya F., and Mousset-Jones P., 1993, "A Method of Designing Auxiliary Ventilation
Systems for Long Single Underground Openings," Proceedings of the 6th US Mine
Ventilation Symposium, SME, Littleton, CO, USA, pp. 245 - 250.
Calizaya F., and Mousset-Jones P., 1997, “Estimation of Leakage Quantity for Long
Auxiliary Ventilation Systems,” Proceedings of the 6th International Mine Ventilation
Congress, SME, Littleton, CO, USA, pp. 475 - 478.
Duckworth I.J., 1999, “Second Year Annual Report,” Unpublished, The University of
Nottingham, October, 23 p.
Duckworth I.J. and Lowndes, I., 2000, "DuctSIM: The Development of a Visual Duct
Simulation Program," 2000 AIME-SME Annual Meeting and Exhibit, SME, Littleton,
CO, USA.
Duckworth I.J. and Lowndes, I., 2001, "The Modelling of Fan and Duct Systems in
Extended Headings," Proceedings of the 7th International Mine Ventilation Congress,
Krakow, Poland.
Gracie A., Howard G., and Job B., 1981, “Analysis of Leaky Auxiliary Ventilation
Systems by Microcomputer,” The Mining Engineer, Vol. 140, No. 236, May, pp. 850 –
851.
Gillies A.D.S. and Wu H.W., 1999, “A Comparison of Air Leakage Prediction
Techniques for Auxiliary Ventilation Ducting Systems,” Proceedings of the 8th US Mine
Ventilation Symposium, University of Missouri-Rolla Press, Rolla, Missouri, USA.
Hall, C.J., 1981, “Mine Ventilation Engineering,” American Institute of Mining,
Metallurgical, and Petroleum Engineers, Inc., Printed by Lucas-Guinn, Hoboken, NJ.
Howden Buffalo, 1999, “Fan Engineering: An Engineer’s Handbook On Fans and their
Applications,” Ninth Edition, Published by Howden Buffalo, Inc., Buffalo, New York.
JM Aerofoil Fans, Bulletin JMA60-99, June 1999.
Le Roux W.L., 1990, “Le Roux’s Notes on Mine Environmental Control,” The Mine
Ventilation Society of South Africa, CTP Book Printers, South Africa.
DuctSIM Design Manual – Version 1.0b – October 2003
43
McPherson, M. J., 1993, “Subsurface Ventilation and Environmental Engineering,”
Published by Chapman & Hall, pp. 134-140.
Meyer C.F., 1990, “Determining the Friction Losses of Underground Ventilation
Ducting,” Journal of the Mine Ventilation Society of South Africa, October, pp. 191 –
196.
Metcalf J.R., 1958, “Leakage in Ventilation Tubing,” Mining Magazine, Vol. 98, No. 5,
May, pp. 274 – 277.
Mine Ventilation Society of South Africa, 1989, “Environmental Engineering in South
African Mines,” Printed by CTP Book Printers, South Africa.
Schauenburg Flexadux Corporation, “Designing a Mine Auxiliary Ventilation System,”
Published Product Literature by Schauenburg Flexadux Corporation, 12 p.
Vutukuri V.S., 1984, "Study of Variables in Auxiliary Ventilation," The Institution of
Mining and Metallurgy, January, pp. A10 – A14.
Vutukuri V.S. and Lama R.D., 1986, “Environmental Engineering Mines” Cambridge
University Press, Melborne.
Vutukuri V.S., 1993, "An Appraisal of the Accuracy of Various Formulas for the Design
of a Simple Auxiliary Ventilation System," Proceedings of the 6th US Mine Ventilation
Symposium, SME, Littleton, CO, USA, pp. 145 - 150.
Wolski J., and Barry J., 1997, "Analysis of Multi-Fan Ventilation Duct Line: Resistance,
Leakage, Fan Performance," Proceedings of the 6th International Mine Ventilation
Symposium, SME, Littleton, CO, USA, pp. 543 - 547.
DuctSIM Design Manual – Version 1.0b – October 2003
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APPENDIX A – MEASURED DATA
Field Measurements
When taking duct measurements in dead-end headings the measurements may be broken into
three main categories:
•
•
•
Airflow Quantity Measurements
Pressure Measurements
Psychrometric Measurements
Airflow Quantity Measurements
Kirchhoff’s First Law states that the mass flow entering a junction equals the mass flow
leaving a junction. It is assumed that the airflow is incompressible, and given that quantity is
equal to mass flow divided by air density (constant in this case), then for a dead-end heading
the airflow entering the heading must equal that leaving the heading. Hence, the airflow in
the duct at any point along the heading is equal to the airflow in the drift or entry.
Considering this, the person taking the measurements has two choices:
1. Measure the airflow in the drift/entry directly using a suitable instrument – such as a
calibrated vane-anemometer.
2. Measure the airflow in the duct. This may be done directly using a suitable instrument
(perhaps a calibrated hot-wire anemometer with extendable probe to push into the
duct), or indirectly by measuring the duct velocity pressure.
It is suggested in this manual that the flow rate in the heading be measured by taking velocity
pressure traverses at discrete points along the duct. Although it is certainly quicker to
measure the airflow directly in the drift/entry, this is generally less accurate, particularly
when there is significant leakage from the duct (which results in turbulent air near the duct).
The flow rate at a particular cross section in a duct can be determined by measuring the local
velocity pressure at a number of fixed points to establish the distribution then integrating over
the area. The velocity profile in the duct will be dependent upon the Reynolds Number,
relative roughness, and upstream disturbances. One of the most common methods to establish
the locations of each fixed point traverse station is to divide the duct into a number of equal
areas and take the measurements at the centre of each. One of the most accurate techniques to
locate the points is the log-linear method, which is based on the velocity profile for fully
turbulent flow. The locations are presented in Table 6.
The velocity pressures are reduced to velocity values using the measured air density, as per
Equation 16. The air velocity values are then converted to a total duct airflow using the
following relationship (where n denotes the number of points per Table 6):
Equation 21 – Duct Air Velocity:
1
Q=A
n
n
∑ ui
i =1
DuctSIM Design Manual – Version 1.0b – October 2003
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Num.
Points
(n)
6
8
12
Location of Measurement Point
Fractions of One Diameter Measured from the Side of the Duct
0.014
0.075
0.021
0.114
0.032
0.117
0.183
0.135
0.184
0.241
0.321
0.345
0.374
0.679
0.655
0.626
0.865
0.816
0.759
0.968
0.883
0.817
0.978
0.886
0.925
0.986
Table 6: Log-linear Traverse Positions in a Circular Duct (after McPherson 1993)
Pressure Measurements
Pressures are measured in the duct using a pitot-static tube, connected to a calibrated micromanometer. The pitot-static device allows the measurement of total, static and velocity
pressure. An explanation of the concept of pressure is provided in Section 3.4.3.2.
The pitot-static tube consists of two concentric tubes. When held facing into the airflow the
inner tube is subjected to the total pressure of the moving airstream. The outer tube is
perforated with a ring of small holes drilled perpendicular to the direction of the airstream.
The outer tube is therefore not influenced by the kinetic energy of the air, and registers the
static pressure only. A manometer connected across the two tappings reports the velocity
pressure.
Psychrometric Measurements
In order to determine the duct air density, it is necessary to measure certain psychrometric air
properties. This would typically consist of the barometric pressure, and the air wet bulb and
dry bulb temperatures. From these values many important properties can be evaluated, not the
least of which is the actual air density. Table 7 provides the process to derive air density from
the measured psychrometric data. It is advised that a spreadsheet be developed to assist with
the calculations, and that calculations be performed in SI units, then converted to Imperial if
necessary. Table 8 provides a list of symbols for the formulae given in Table 7.
Step
1
2
Description
Latent heat of
evaporation
Saturated vapour
pressure
Equation
Units
L = ( 2502.5 − 2.386t ) × 1000
J/kg
For Lw, use tw. For Lws, use tws.
esError! Bookmark not defined.
Pa
 17.27t 
= 610.6exp

 t + 237.3 
For esw, use tw. For esd, use td.
3
4
5
6
7
Actual vapour pressure
(from X and P)
Actual vapour pressure
(from P, td, and tw)
Moisture content
Gas constant of
unsaturated air
Specific heat of
unsaturated air
e=
Pa
PX
X + 0.622
(
Cpa P td - tw
0.622 L
e
X = 0.622
P−e
R + XRv
Rm = a
X +1
e = esw −
Cpm =
Cpa + XCpv
)
Pa
kg/kg dry
J/kgK
J/kgK
X +1
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Step
8
9
Description
Actual density of air
(from P, e, td)
Apparent density of air
Equation
10
Relative humidity
rh =
11
12
Enthalpy
Sigma Heat
H = Cpatd + X[Cwtw + L + Cpv(td - tw)]
S = H - XCwtw
ρ
P − 0.378e
=
(
)
Units
kg moist air/m3
Ra t d + 27315
.
ρapp =
P−e
Ra ( t d + 27315
. )
e
× 100%
esd
Kg dry air/m3
%
J/kg dry air
J/kg dry air
Table 7: Psychrometric Relationships
Symbol
Cpa
Cpm
Cpv
Cw
E
es
esd
esw
H
Lw
Lws
P
Ra
Rm
Rv
Rh
ρ
ρapp
S
td
tw
tws
X
Description
Specific heat of dry air at constant pressure
Specific heat of unsaturated air
Specific heat of water vapour at constant pressure
Specific heat of liquid water
Actual vapour pressure
Saturated vapour pressure
Saturated vapour pressure at dry bulb temperature
Saturated vapour pressure at wet bulb temperature
Enthalpy
Latent heat of evaporation at wet bulb temperature
Latent heat of evaporation at wet surface temperature
Barometric pressure
Gas constant for dry air
Gas constant for unsaturated air
Gas constant for water vapour
Relative humidity
Density of unsaturated air
Apparent density
Sigma heat
dry bulb temperature
wet bulb temperature
wet surface temperature
Moisture content
Units
J/kgK
J/kgK
J/kgK
J/kgK
Pa
Pa
Pa
Pa
J/kg dry air
J/kg
J/kg
Pa
J/kgK
J/kgK
J/kgK
%
kg/m3
kg dry air/m3
J/kg dry air
°C
°C
°C
kg moisture/kg dry
Table 8: List of Symbols for the Psychrometric Calculations
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APPENDIX B – DUCTCON PROGRAM
The Ductcon program has been developed to facilitate the reduction of duct field data. This is
an ancillary application for Ductsim, however the program is entirely discrete. The output
includes important duct leakage and resistance constants. These constants may then be used
in the Ductsim program.
The theory used in the Ductsim program is detailed in the main body of the manual. The main
equations include Equation 3 (Atkinson’s Equation), Equation 14 (Woronin’s Equation), and
Equation 15 (Browning’s Formula).
The application consists of two main views, termed the Input View and the Results View.
Ductcon Input Data
Duct data are input using the Add Duct Data dialog box. Either selecting Duct/Add Data from
the menu, or pressing the “Add” button on the toolbar accesses this. An example for this
dialog box is shown in Figure 34.
Figure 34: Ductcon Add Duct Data Dialog Box
The user is required to enter the duct diameter and segment length, and then measured airflow
and pressure data for each end of the duct segment. The following rules must be adhered to
when inputting the data:
1.
2.
3.
4.
5.
A section of duct without any fans should be used.
The points should be chosen such that the quantity at point 1 is higher than point 2.
The quantity values must be positive.
The pressure at point 1 must be greater than point 2.
The pressure values must be positive.
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48
6. The pressure values should be the gauge total pressure (average) measured at each
station.
The above rules are for a forcing duct system, where the quantity and duct wall pressure both
reduce as the distance along the duct increases. The program can be used for exhausting ducts
by entering the negative duct pressures as positive values (so that the higher pressure still
corresponds to the higher quantity).
Input View
As ducts are added, they are listed in the Input View. These ducts may be edited or deleted
from the project either using the Duct Menu, or the Edit and Delete buttons on the toolbar.
An example for the Input View is shown in Figure 35. Listed in the table are the duct
description, length, diameter, quantity and pressure data.
Figure 35: Ductcon Input View
Ductcon Results
Calculations are automatically conducted as each duct is added to the project. The results are
presented in the Results View (see Figure 36). The following results are included:
1. Area of the duct.
2. Resistance of the duct per 100m (100ft) – based on Browning (1983) approximation
(see Equation 15).
3. Atkinson friction factor – evaluated from resistance of the duct per 100m (100ft) and
the geometry of the duct (see Equation 3).
4. Resistance of the leakage paths per 100 m – based on Woronin’s Equation (see
Equation 14).
5. The leakage constant for the duct – Lc based on Browning (1983) approximation (see
Equation 22).
Equation 22 – Leakage Coefficient: L c =
3(Q1 - Q 2 ) (P1 - P2 )
2L(P11.5 - P21.5 )
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Figure 36: Ductcon Results View
The Ductsim program requires that the user enter leakage data in terms of the resistance of
the leakage paths per 100m (100ft) of duct. Although the leakage coefficient provided in
Ductcon cannot be input to Ductsim, it provides an excellent parameter for quantifying the
quality the quality of a duct installation. Le Roux (1990) provides a range for the leakage
coefficient, which is:
•
•
•
•
Excellent Duct
Good Duct
Poor Duct
Bad Duct
= 0.03
< 0.25
= 0.5
> 1.0
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